2024/01/17 by Nemanja Poznanović, Cheryl E. Praeger, Poznanovic, Nemanja +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2401.08907
openalex publication_date 2024/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let OG(4) denote the family of all graph-group pairs (Γ, G) where Γ is finite, 4-valent, connected, and G-oriented (G-half-arc-transitive). A subfamily of OG(4) has recently been identified as `basic' in the sense that all graphs in this family are normal covers of at least one basic member. In this paper we provide a description of such basic pairs which have at least one G-normal quotient which is isomorphic to a cycle graph. In doing so, we produce many new infinite families of examples and solve several problems posed in the recent literature on this topic. This result completes a research project aiming to provide a description of all basic pairs in OG(4).